Explicit Formula for Predictive FIR Filters and Differentiators Using Hahn Orthogonal Polynomials

Authors:
Saed Samadi;Akinori Nishihara
Affiliations:
-;-
Venue:
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Year:
2007

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Abstract

An explicit expression for the impulse response coefficients of the predictive FIR digital filters is derived. The formula specifies a four-parameter family of smoothing FIR digital filters containing the Savitsky-Goaly filters, the Heinonen-Neuvo polynomial predictors, and the smoothing differentiators of arbitrary integer orders. The Hahn polynomials, which are orthogonal with respect to a discrete variable, are the main tool employed in the derivation of the formula. A recursive formula for the computation of the transfer function of the filters, which is the z-transform of a terminated sequence of polynomial ordinates, is also introduced. The formula can be used to design structures with low computational complexity for filters of any order.